In the second chapter of our book, we had dealt with the shape, size and age of the universe as propounded by different scientists and in the third chapter we had a detailed discussion about these aspects of *Loka *(universe) as described by the Jain philosophy. Now, we are in a position to compare and contrast them.

Taking first the Einstein's cylindrical universe, in which the space is so curved that it forms a closed and finite universe, the similarity becomes striking. Both (Einstein's universe and Jain's Loka) are finite. In Jain Loka, the shape of the universe as inferred on the basis of the fundamental dimensions given in the works on Jain Cosmology is curved (see supra, p. 159). The space of the Einsteinian universe is also curved. But whereas in Einstein's universe the space itself is finite, in the case of Jain's Loka, the space is infinite but the universe is finite. The principle of positive and negative ethers explains logically the finiteness of the universe.

In Einstein's concept, the space is totally occupied by matter; there is no scope for the vacuum. According to the original field equations of 1915, the space would not exist if it was not occupied by any matter. Describing Einstein's modification of his field equations, Prof. Whittaker observes: "Under the influence of Mach's doctrine, Einstein made an important modification of the field-equations of gravitation. He now objected to his original equations of 1915 on the ground that they possessed a solution even when the universe was supposed void of matter, and he added a term-the 'cosmological term' as it is called-with the idea of making such a solution impossible. After a time it was found that the new term did not do what it had been designed to do, for the modified field-equations still possessed a solution-the celebrated 'De Sitter World'-even when no matter was present; but the De Sitter World was found to be so excellent an addition to the theory that it was adopted permanently, and with it, of course, the cosmological term in the field-equations: so that this term has been retained for exactly the opposite reason to that for which it was originally introduced."^{[1]}

From this, we may conclude that by adding the cosmological term in the original field-equations of Einstein, we get exactly the opposite result. It means that Einstein's world which was thought to be fully occupied space turned into one which was possible even when not occupied. Such space was then called De Sitter World.

Now when we compare the concepts of *Loka-ākāśa *and *Aloka-ākāśa *with Einstein's World and De Sitter World respectively, we see that the former represents *Loka-ākāśa *which is always occupied by *pudgala *and the latter represents De Sitter World which is empty space. In other words, the 'cosmological term' added in the original field-equations is comparable to *Aloka-ākāśa*, while the original field-equations are comparable to *Lokāloka-ākāśa *(i.e. *Ākāśāstikāya*) which is a combination of Einsteinian World and De Sitter World.

As far as the curvature of the world is concerned, a problem is created before the scientists on account of the solutions of the field-equations of the universe-whether the curvature is positive or negative. If the curvature is positive, the universe would be finite and closed and if the curvature is negative, then the universe would be infinite and open. The space of the Einsteinian World is positive and hence, the universe is finite and closed. On the basis of the solutions of the field equations, it is also possible that the curvature is negative. In that case, the infinite and open universe also has been conceived. Thus, on the basis of +ve and -ve curvatures respectively, there are two possible concepts of universe-'finite and closed' and 'infinite and open'. Now, if we assume that the curvature of *Lokākāśa *is +ve and that of the *Alokākāśa *is -ve, then the finiteness of the *Lokākāśa *and infiniteness of *Alokākāśa *are possible. Thus, the Jain theory of *Lokākāśa *and *Alokākāśa *is a combination of the two cosmological theories which accept +ve and ve curvature of space.

Prof. G. R. Jain, comparing the Einsteinian World with the Jain *Loka*, writes: "Now coming to the next point, viz., the existence of these substances (media) within the confines of the *Loka *and not beyond, we find that this is much more reasonable and satisfactory assumption than Einstein's finite universe 'with no space beyond a certain space'. According to Einstein's Cylinder theory, neither the universe had a beginning nor will it ever come to an end. In other words, it is a stable unit. If we regard our universe as infinite it cannot be stable at the same time, for in that case we can think the infinite space to be filled with a number of universes and their attractions on our universe would scatter it into infinite space. In order, therefore, to maintain the stability of our universe running from an infinite past into an infinite future the universe was conceived as of finite dimensions, but since mathematical conditions negate the idea of a void beyond finite universe, the whole space was taken to constitute the finite universe.

"The Jaina concept is more comprehensive because the stability of the universe is maintained by saying that there are no media of motion and rest beyond a certain limit and consequently matter or energy can never go out of it, i.e., the total energy of the universe will ever remain constant. Further, since Jainism regards space as a reality, there is no void beyond *Loka *but only one substance-pure space and nothing else. All the difficulties are thus ingeniously overcome."^{[2]}

The concept of Einsteinian cylindrical universe is subjected to review in the scientific world. Whereas some scientists have supported it, others have made strong criticism of it. Someone has remarked that the Einstein's Universe cannot be easily visualised. H. Ward has gone to the extent of saying that it is quite inconceivable to think that beyond a certain jumping-off boundary there is no space, and the mathematicians are not able to unmake there brain and visualize finite space.^{[3]}

Similarly, other famous writers have remarked that the concept of "nothing" beyond a limit is self-contradictory.^{[4]}

An argument is given against the finite space as conceived by Einstein as follows: "In Einstein's universe, there is 'nothing' beyond the universe. The concept of 'empty space' is not accepted by it. But whereas regarding time, it is believed that it is inconceivable that there was once a moment with no moment preceding it, how is it not inconceivable to think of a limit beyond which there is no space?"^{[5]}

Again, an effort has been made to refute this argument and prove that space can be finite. Whittaker puts it this way: "Those who oppose the concept of finite space they fail to comprehend the difference between 'finite' and 'bounded'. The space of the non-Euclidean geometry, whose curvature is +ve is finite. It means that such space has a definite volume, which can be described as a definite number of cubic miles, but it has not boundary. It is not that at a certain place, the space comes to an end, and there is nothing beyond it. This difference between 'finiteness' and 'boundedness' is comprehensible to the mathematician, but difficult for a layman to conceive it......In a universe such as the Einstein world, whose curvature is positive and is everywhere the same, there are no Euclidean straight lines, but the paths of rays of light play much the same part as straight lines do in Euclidean geometry: the chief difference between them and Euclidean straight lines is that they return into themselves (like the equator on a sphere) after having made a complete circuit of the world. We should therefore in principle be able to see our own backs by means of light which has been all round the universe: but certain features in the situation, into which we need not here enter, prevent the observation being made.

"Since every ray of light returns into itself, we see that no ray can meet a frontier of the space, and therefore that the space can have no frontiers."^{[6]}

If we consider this problem in the light of the Jain theory of *Lokākāśa *and *Alokākāśa*, we find that a solution is possible: It becomes quite conceivable and logical to think that beyond the boundary of the universe, there is no medium of motion, and hence, no particle of matter or energy can go beyond that. Also a ray of light would simply be reflected at the boundary.^{[7]}

Einstein, however, has given an illustration to explain how the universe (space) is finite, but not bounded: ' On this, perhaps the most interesting question of all, present science is unfortunately noncommittal. The reason lies in the uncertainties which still surround the exact form of the metric, *dS*2, for it is by an appeal to the detailed mathematical structure of this quantity that the decision as to the finiteness of time and space must ultimately be made. To specify *dS*^{2} is not, as Poincare would have it, a matter of convenience alone. Einstein has taught us what is meant by the corrext metric, and there is very little doubt that we should recognize it as correct if sufficient observational data were at hand. These data are chiefly astronomical and are difficult to obtain; their desirability was prime motivation for the construction of the great telescope at Mt. Palomar. Of the detailed forms so far proposed for *dS*2 perhaps the most successful ones imply a finite space-time. Some suggest a finite space and an infinite time; some are finite in both components."^{[8]}

Prof. Margenau explains this thus: "The Murkowski metric used in the special theory of relativity is infinite in both. It is satisfactory for all terrestrial purposes and comes closest to habitual institution. But it seems certain to fail in the far reaches of the universe where the galaxies exhibit their renowned runaway motions. According to some theories, finite space can account for the recession of the distant nebulae.

"Avoiding all detail, we shall merely consider here the questions so frequently asked: What is meant by a finite space? If space is finite, what is beyond it? Poincare's example should answer them. We gave it in its two-dimensional form on page 134. Let us return to it in three dimensions. Our universe is then a large sphere with a radial distribution of temperatures, and *T *= o at the boundary. All objects have sizes proportional to *T*, and we have supposedly no sense of temperature, no sight. (Poincare takes care of visual observation by postulating a special form for the index of refraction; we ignore this complication). As we move toward the boundary, our own bodies, together with the objects we pass, are reduced in size but we are ignorant of all these changes. Our speed, though apparently the same, is actually diminished, and we never reach the boundary. If we relied on appearances, we should call our universe infinite. To be sure, there would be space beyond it, but that space would be inaccessible to us.

"Another example, due to Einstein, will show how space can be finite and yet have no space beyond it. He invites us to consider a circle whose circumference is infested by creatures having cognizance of only one dimension. They can move fore and aft; left and right, up and down are unknown to them. Let the circle be very large, or else let there be no signposts telling the creatures whether they have been at a given point before. They will then conclude, after a great deal of crawling, that their world if infinite and extends in one dimension.

"As animal of somewhat higher order, able to know two dimensions, will recognize the error made. It will say to the one-track creature: 'You don't know this because you observations were confined to one dimension'. Note that there is no one-dimensional space behind that of the creatures; the beyond is two-dimensional space behind that of the creatures; the beyond is two-dimensional and therefore truely inaccessible to them.

Now let the two-track animal roam upon the surface of a three-dimensional sphere. Under analogous circumstances, it will conclude that its space is infinite in two dimensions. But man, with his superior wisdom, informs it that its space is really finite but curved in three dimensions.

Who will say that man's three-dimensional space, deemed infinite by him, is not finite but curved in four dimensions?"^{[9]}

The illustration given by Poincare intends to show that due to the gradual decrease in the temperature as we go nearer to the boundary of the universe, our velocity and expansion would slow down. The result would be that we shall never be able to reach the boundary of the universe. There is a very similar concept in Jain cosmology, in which it is asserted that the *pudgalas *near the boundary of the *Lokākāśa*, by nature, are "*abaddha-pārśva-spṛṣṭa*" (are neither bound nor touched by other *rukṣa pudgalas *i.e., negatively charged particles) and become *rukṣa *themselves, so that the soul and *pudgalas *cannot transcend the boundary of the *Loka*. This is the Cosmic Law of Nature.^{[10]} Although it is rather difficult to comprehend exactly what is meant by *abaddha-pārśva-spṛṣṭa*, yet it can be said that it is a natural phenomenon on account of which the *pudgalas *(material particles as well as waves) would ultimately become "*rukṣa*"^{[11]} (negatively charged) and thus would lose their capacity to move further. Now if we compare Poincare's statement quoted above with the concept of Jain cosmology, there is a striking similarity between them. The "*abaddha-pārśva-spṛṣṭa"* and *rukṣa pudgalas *are comparable with the physical objects having absolute zero temperature. In Poincare's illustration, such objects explain how the nature of space which is finite does not allow them to reach the cosmic boundary and thus they remain confined to the finite universe. In Jain *Lokākāśa*, the nature of the *pudgalas *does not allow them to reach the end of the *Loka*. The Jain cosmology has clearly mentioned that the *Dharmāstikāya *and the *Adharmāstikāya *do not exist in *Alokākāśa*, and hence, no motion whatsoever is possible in the supracosmic space, and at the same time because of the *rukṣa *nature of the *pudgalas *they cannot reach the boundary of the *Loka*. One can easily see the logical soundness of Jain theory to explain the finiteness of the cosmic space, and infiniteness of supracosmic space. Further, when we examine the concept of *Alokākāśa*, we at once can comprehend its truthfulness. Whereas Einstein's finite space cannot be visualised easily, there is no difficulty in comprehending finite *Loka *and infinite *Aloka*.

The concept of 'Aloka' is also proved by the fact, that^{[12]} "space could only be of literally infinite extent if it contained no matter at all." This means that in absence of matter, the space does not become curved but extends to infinity. This is exactly what happens in Aloka. Another fact, supporting the concept of Aloka, is "if we relied on appearances, we would call our universe infinite. To be sure, there would be space beyond it but that space would be inaccessible to us."^{[13]} This exactly conveys the same idea that in absence of the media of motion the space beyond the universe is inaccessible to us.

Secondly, we take the case of expanding universe. The concept of the expanding universe has become quite popular recently. The Jain's theory of universe obviously rejects the process of expansion of space. The first argument against it is that space cannot expand, firstly, because it is immobile, and secondly, because space itself is infinite i.e., there is no place where there is no space. The second argument against it is that even if we consider space to be finite, in what it will expand? How can it expand in "nothingÕ? Besides these questions the already discussed scientific arguments against the theory of expanding universe also make the theory quite uncertain. We suggest that some other explanations of the red shift of the spectral lines should be tried to find out.

Finally, we may conclude our comparison of Einstein's view with the Jain view regarding the shape and size of the universe by saying that there are more similarities, and less difference in them. The main differences are-

1. In Jain view, the total space is infinite and a single entity; only *lokākāśa *is finite and has a definite shape, which has a natural curve. In Einstein's view, the entire space itself is finite.

2. The geometry of cosmic space of the Jain *Loka *may be non-Euclidean; the space of Einsteinian universe is non- Euclidean.

3. There is curvature in the cosmic space of the Jain *Loka *whereas the whole space is curved in Einsteinian world.

Now, we come to the time-aspect of both views. Both views are almost identical-both consider the universe to be beginning less and endless, i.e., the universe is eternal with respect to time. In Einsteinian universe, the dimension of time is infinite at both ends; in Jain cosmological view, both *Loka *and *Aloka *are eternal (i.e., beginningless and endless). Thus, the same fact has been expressed in different terminology. Thus, these two cosmological theories-Einsteinian and Jain philosophical- stand against other views which believe in beginning and end of the universe.

*From Euclid to Eddington*, p. 126.

*Cosmology: Old and New*, pp. 96-97.

*Exploring the Universe*, by H. Ward, p. 16.

*From Euclid to Eddington*, p. 188.

*The Nature of the Physical World*, by Prof. A. S. Eddington, p. 137.

*From Euclid to Eddington*, p. 188.

In fact, it is propounded in the Jain canonical texts that sound-*pudgalas *can reach the end of the *Lokākāśa*, beyond which they cannot travel in the *Alokākāśa*, and would get reflected. (See, *Pa*ṇṇ*avaṇā*, *pada *XI).

See A. Einstein, "*The Meaning of Relativity*", Princeton University Press, Princeton, N.J., 1946.

*The Nature of Physical Reality*, by Prof. Henry Margenua, pp. 164, 165.

*savvesuvi ṇaṃ logaṃttesu abaddhapāsapuṭṭhā poggalā lukkhatāe kajjaṃti jeṇaṃ*

*jīva ya poggalā ya no saṃcāyaṃti bahiyā logaṃtā gamaṇayāe evaṃppegā*

*logṭṭhiti paṇattā*. - *Ṭhāṇaṃ *10.1.

In our interpretation, *snigdha *and *rukṣa *respectively stand for +ve and -ve electrical charges. Cf. *Microcosmology: Atom in the Jain Philosophy and the Modern Science *by Jethalal S. Zaveri & Muni Mahendra Kumar, p. 192.

Fom a lecture on the '*The Expanding Universe*', delivered at Science Congress Bombay, 1933 by Prof. A. C. Benerji.

*The Nature of Physical Reality*, by Prof. Henry Margenau, p. 164.